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A numerical study of pulsatile laminar flows in a pipe with a ring‐type constriction
Author(s) -
Shi Z. D.,
Lee T. S.,
Winoto S. H.
Publication year - 1995
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650200403
Subject(s) - pulsatile flow , laminar flow , strouhal number , mechanics , reynolds number , pressure gradient , mathematics , flow (mathematics) , hele shaw flow , physics , open channel flow , turbulence , medicine , cardiology
Numerical simulations have been carried out to study pulsatile laminar flows in a pipe with an axisymmetric ringtype constriction. Three types of pulsatile flows were investigated, namely a physiological flow, a pure sinusoidal flow and a non‐zero mean velocity sinusoidal flow. The laminar flow governing equations were solved by the SIMPLE algorithm on a non‐staggered grid and a modified Crank‐Nicolson approximation was used to discretrize the momentum equations with respect to time. The maximum flow Reynolds numer ( Re ) is 100. The Womersley number ( N w ) ranges from 0 to 50, with the corresponding Strouhal number ( St ) ranging from 0 to 3·98. The constriction opening ratio ( d/D ) and thickness ratio ( h/D ) are fixed at 0·5 and 0·1 respectively. Within the time period investigated, all these pulsatile flows include both forward and backward flows. The unsteady recirculation region and the recirculation points change in size and location with time. For N w ≤ 1 and St≤ 1·56 x 10 −3 the three pulsatile flows have the same simple relation between the instantaneous flow rate and pressure loss (Δ p ) across the constriction and the pressure gradient in the axial direction (d p /dz) in the fully developed flow region. The phase angles between the flow rate and pressure loss and the pressure gradient are equal to zero. With increasing N w and St , the phase angle between the flow rate and the d p /dz becomes larger and has its maximum value of 90° at N w = 50 and St = 3·98. The three pulsatile flows also show different relations between the flow rate and the pressure gradient. The pure sinusoidal flow has the largest maximum pressure gradient and the non‐zero mean velocity sinusoidal flow has the smallest. For larger N w and St the fully developed velocity profiles in the fully developed flow region have a smaller velocity gradient along the radial direction in the central region. The maximum recirculation length increases for N w ranging from 0 to 4·2, while this length becomes very small at N w = 50 and St = 3·98. The deceleration tends to enlarge the recirculation region and this effect appears for N w ≥ 3 and St ≥ 1·43×10 −2 . Linear relations exist between the flow rate and the instantaneous maximum values of velocity, vorticity and shear stress.